Cosmological α-attractors stand out as particularly compelling models to describe inflation in the very early universe, naturally meeting tight observational bounds from cosmic microwave background (CMB) experiments. We investigate α-attractor potentials in the presence of an inflection point, leading to enhanced curvature perturbations on small scales. We study both single- and multi-field models, driven by scalar fields living on a hyperbolic field space. In the single-field case, ultra-slow-roll dynamics at the inflection point is responsible for the growth of the power spectrum, while in the multi-field set-up we study the effect of geometrical destabilisation and non-geodesic motion in field space. The two mechanisms can in principle be distinguished through the spectral shape of the resulting scalar power spectrum on small scales. These enhanced scalar perturbations can lead to primordial black hole (PBH) production and second-order gravitational wave (GW) generation. Due to the existence of universal predictions in α-attractors, consistency with current CMB constraints on the large-scale spectral tilt implies that PBHs can only be produced with masses smaller than 108 g and are accompanied by ultra-high frequency GWs, with a peak expected to be at frequencies of order 10 kHz or above.

With an energy scale that can be as high as 10 14 GeV, inflation may provide a unique probe of high-energy physics. Both scalar and tensor fluctuations generated during this early accelerated expansion contain crucial information about the particle content of the primordial universe. The advent of ground-and space-based interferometers enables us to probe primordial physics at length-scales much smaller than current CMB constraints. One key prediction of single-field slow-roll inflation is a red-tilted gravitational wave spectrum, currently inaccessible at interferometer scales. Interferometers probe directly inflationary physics that deviates from the minimal scenario and in particular additional particle content with sizeable couplings to the inflaton field. We adopt here an effective description for such fields and focus on the case of extra spin-2 fields. We find that time-dependent sound speeds for the helicity-2 modes can generate primordial gravitational waves with a blue-tilted spectrum, potentially detectable at interferometer scales.

We investigate small-scale signatures of the inflationary particle content. We consider the case of a light spin-2 particle sourcing primordial gravitational waves by employing an effective field theory description. Upon allowing time-dependent sound speeds for the helicity modes, this setup delivers a blue tensor spectrum detectable, for example, by upcoming laser interferometers. Our focus is on the tensor non-Gaussianities that ensue from this field configuration. After characterising the bispectrum amplitude and shape-function at CMB scales, we move on to smaller scales where anisotropies induced in the tensor power spectrum by long-short modes coupling become the key handle on (squeezed) primordial non-Gaussianities. We identify the parameter space generating percent level anisotropies at scales soon to be probed by SKA and LISA.

The Laser Interferometer Space Antenna (LISA) has two scientific objectives of cosmological focus: to probe the expansion rate of the universe, and to understand stochastic gravitational-wave backgrounds and their implications for early universe and particle physics, from the MeV to the Planck scale. However, the range of potential cosmological applications of gravitational-wave observations extends well beyond these two objectives. This publication presents a summary of the state of the art in LISA cosmology, theory and methods, and identifies new opportunities to use gravitational-wave observations by LISA to probe the universe.